Discussion
When is the value of information zero?
Answer: C
If the same action is optimal whatever the observation turns out to be, learning it changes nothing and its value is zero. Independence from utility is a sufficient condition but not the general criterion, certainty of confirmation is a special case, and cost is compared against the value rather than making it zero. Asking whether an answer would change what one does, before paying to obtain it, is a discipline that applies far beyond formal decision theory.
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